Modern Physics Letters B

In this paper we review recent progress in studying quantum phase transitions in one- and two-component Bose–Einstein condensates (BEC) in optical lattices. These phase transitions involve the emergence and disappearance of quantum coherence over the whole optical lattice and of linear superposition of macroscopic quantum states. The latter may provide new means to engineer and manipulate novel macroscopic quantum states and novel coherent atomic beams for quantum information processing, quantum computing and other purposes.

We have studied a correlated fermion model with nearest neighbor attractive interactions on a square lattice by means of quantum Monte Carlo simulation. At half-filling this model exhibits rather strong correlation effects. Charge fluctuations are suppressed and the ground state is an insulator with long-range anitferromagnetic correlations. When doped with holes this model exihibits phase separation which seems to be triggered by the antiferromagnetic long-range correlations.

The binding energy of an exciton in the GaAs/AlAs quantum well is discussed including the influence of interface optical phonons and bulk longitudinal optical phonons confined in the well under hydrostatic pressure. The dependence of the phonon energies on pressure is considered using a linear interpolation method to obtain the pressure effect on the exciton binding energy by a variational calculation. The result shows that the polaronic effect on the exciton binding energies cannot be neglected and the pressure effect on the exciton-phonon interaction is obvious.

Using the t′-J model, we study the effects of skyrmions in doped antiferromagnets. For the π flux phase, the low energy effective theory of the t′-J model can be mapped onto N=2 2+1Dσ₃-quantum electrodynamics. There exist fermion zero modes around skyrmions. Two holons of different sublattices are bound onto skyrmions as a bosonic composite object.

The nanomechanical properties of small fullerenes (C20, C36, C60 and C70) compressed between graphite planes are investigated based on molecular dynamics (MD) simulation using a combination of the many-body Brenner potential with a two-body potential. We find all the fullerenes exhibit similar elastic behavior even if the minimum radii of clusters in the direction of compression are reduced to 1/3 or 1/2 that of the free clusters. Both the potential energy of the system and restoring pressure on the graphite planes as functions of the axial strain are found to be reversible. This is a result of the reversible structure change. The fullerene is deformed severely into a disc-like structure due to compression. The deformation is almost saturated. In the process of decompression the free-fluerene structure is returned, and the cage rotated slightly between graphite sheets. To compare the elasticity of different fullerenes, the second order derivative of strain energy to strain is approximately calculated as a Young's modulus. The modulus becomes larger with increasing fullerene size.

The phase transition of DNA molecules is studied in an exactly solvable formalism with the Morse and Deng–Fan potentials for the interstrand hydrogen bonds of nucleotide base pairs. It is shown that although the two potentials have different short-range behaviors, the thermodynamic quantities of the DNA system in these potentials enjoy the same scaling laws with the associated critical exponents, which are explicitly calculated. These exactly solvable DNA models are shown to exhibit a phase transition of the second order and the results of the analysis agree with previous studies.